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Abstract:

This invention relates to optical systems for holographic projectors. We
describe a holographic image projection system, the system including: a
spatial light modulator (SLM) for displaying a hologram; first optics to
provide an input beam to said SLM; second optics to process an output
beam from said SLM to provide a displayed image; and a hologram processor
to receive image data for display and to output data to said SLM to
display a hologram to provide said displayed image; and wherein at least
one lens of said first optics or said second optics is encoded in said
hologram.

Claims:

1. A holographic image projection system, the system comprising:a spatial
light modulator (SLM) for displaying a hologram;first optics to provide
an input beam to said SLM;second optics to process an output beam from
said SLM to provide a displayed image; anda hologram processor to receive
image data for display and to output data to said SLM to display a
hologram to provide said displayed image; andwherein at least one lens of
said first optics or said second optics is encoded in said hologram.

2. A holographic image projection system as claimed in claim 1 wherein
said first optics comprises collimation optics, and wherein said at least
one encoded lens comprises a collimation lens of said collimation optics.

3. A holographic image projection system as claimed in claim 2 wherein
said first optics comprises beam expansion optics including said
collimation optics.

4. A holographic image projection system as claimed in claim 1 wherein at
least one lens of said first optics and at least one lens of said second
optics is encoded in said hologram.

5. A holographic image projection system as claimed in claim 4 further
comprising a mirror configured such that said input beam and said output
beam of said SLM are on the same side of said SLM, wherein said second
optics comprises demagnification optics, and wherein at least one lens of
said first optics and at least one lens of said second optics is encoded
in said hologram.

6. A holographic image projection system as claimed in claim 5 wherein
said SLM comprises a reflective SLM.

7. A holographic image projection system as claimed in claim 4 wherein
said second optics comprises a single physical lens.

8. A holographic image projection system as claimed in claim 7 wherein
said first optics comprises said single physical lens, said single
physical lens being shared with said second optics.

9. A holographic image projection system as claimed in claim 1 wherein
said second optics has a variable optical power.

10. A holographic image projection system as claimed in claim 9 wherein
said second optics comprises a variable physical lens, and wherein said
at least one lens encoded by said hologram processor comprises a variable
focus lens of said second optics.

12. A holographic image projection system as claimed in claim 1 wherein
said hologram comprises a Fresnel hologram.

13. A holographic image projection system as claimed in claim 1 wherein
said SLM comprises a liquid crystal SLM.

14. A holographic image projection system as claimed in claim 1 wherein
said hologram processor is configured to generate a plurality of temporal
holographic sub-frames for a single said displayed image.

15. An optical module for a holographic projection system, the module
comprising:an optical input;a spatial light modulator (SLM) for
displaying a hologram, said SLM having an input optical path from said
optical input passing through said SLM to provide a modulatable optical
output;a reflector to one side of SLM such that said optical path through
said SLM passes through said SLM twice, said optical input to said SLM
and said optical output from said SLM being on the same side of said SLM;
anddemagnification optics coupled to said modulatable optical output to
enlarge an image generated by a hologram modulating said SLM.

17. An optical module as claimed in claim 15 wherein said demagnification
optics comprises a single lens.

18. An optical module as claimed in claim 17 wherein said single lens is
located in said optical path between said optical input and said SLM.

19. An optical module as claimed in claim 15 wherein said input optical
path to said optical SLM and said optical output from said SLM have a
portion of shared optical path, the system further comprising a polariser
in said portion of shared optical path.

21. An optical module as claimed in claim 15 wherein said optical input
comprises an optical light guide, and wherein said input optical path
diverges from an output of said optical light guide up to said SLM.

Description:

[0002]Many small, portable consumer electronic devices incorporate a
graphical image display, generally a LCD (Liquid Crystal Display) screen.
These include digital cameras, mobile phones, personal digital
assistants/organisers, portable music devices such as the IPOD®,
portable video devices, laptop computers and the like. In many cases it
would be advantageous to be able to provide a larger and/or projected
image but to date this has not been possible, primarily because of the
size of the optical system needed for such a display. Use of a
holographic projector offers a potential solution to this problem but it
would be desirable to be able to implement such a system in a relatively
confined space.

SUMMARY OF THE INVENTION

[0003]According to the present invention there is therefore provided a
holographic image projection system, the system comprising: a spatial
light modulator (SLM) for displaying a hologram; first optics to provide
an input beam to said SLM; second optics to process an output beam from
said SLM to provide a displayed image; and a hologram processor to
receive image data for display and to output data to said SLM to display
a hologram to provide said displayed image; and wherein at least one lens
of said first optics or said second optics is encoded in said hologram.

[0004]In embodiments by encoding at least one of the lenses into the
hologram the size of the optical system is reduced. The lens which is
encoded in the hologram preferably comprises a lens which, in a
conventional configuration, would be adjacent the hologram, such as lens
L2 or lens L3 of FIG. 2. Thus the lens may comprise a
collimation lens (collimation optics) of the first optics, for example
forming part of a beam expander or Keplerian telescope and/or a lens of
demagnification optics for the hologram.

[0005]The one or more lenses encoded in the hologram may comprise either a
simple lens or a compound lens, and in embodiments an encoded lens may
have a complex optical configuration, for example to correct for
aberrations or distortions. In particular, the encoded lens may, for
example, compensate for light source (laser) divergence and/or beam shape
(for example elliptical rather than circular). Thus in embodiments the
encoded lens may be an anamorphic lens.

[0006]In some particularly preferred embodiments two lenses are encoded
into the hologram, one for the first optics and another for the second
optics. This, in effect, folds the configuration of FIG. 2 back on itself
so that preferably these two lenses in fact comprise a single, shared
lens with a reflecting surface being placed on the opposite side of the
hologram (spatial light modulator) to the optics. In the example
arrangement of FIG. 2, therefore, the functions of L2 and L3
are performed by a single, common lens encoded in the hologram.
Preferably the SLM comprises a reflective SLM to avoid the need for a
separate reflecting surface.

[0007]In some particularly preferred embodiments the second
(demagnification) optics comprises a single physical lens. This may
either be shared with the first (beam expanding) optics or the first lens
(L1 in FIG. 2) may be omitted and a diverging light source employed.
In either case it will be appreciated that a holographic optical
projection module may be constructed with just a single lens in addition
to the spatial light modulator (hologram).

[0008]In a system with a single lens preferably the SLM modifies, for
example rotates, the polarisation of the modulator light. Thus preferably
the SLM comprises a liquid crystal SLM, for example a ferroelectric
liquid crystal SLM. In such an arrangement a polariser is preferably
included to, in effect, separate the input and output beams to and from
the SLM; this polariser may be either linear or circular. Conveniently
the polariser may comprise a polarising beam splitter. In this case the
input and output optical paths for the holographic optical projection
module can be configured to be at substantially 90 degrees to one
another, for example a polarising beam splitter directing the output
light for a displayed image out at 90 degrees to a normal to the surface
of the spatial light modulator.

[0009]In embodiments where a (first) lens of the beam expander is encoded
into the hologram a further advantage arises in that the power of the
encoded lens may be altered by altering the pattern of modulation of the
SLM. In other words the encoded lens may be a lens of controllable
optical power (focal length), in which case variable demagnification may
be applied to control the size of the displayed image. In such an
arrangement the demagnification optics is preferably adjustable to take
account of the variable optical power of the lens encoded into the
hologram, for example by making a second lens of the demagnifying optics
movable (along an optical axis) or variable, more particularly of
variable focal length. A range of different technologies is available to
provide such a variable power lens. In preferred embodiments the
demagnifying optics, more particularly the power of the second lens, is
electrically controlled by the hologram processor in conjunction with the
power of the encoded lens to control the size of the displayed image.

[0010]The hologram preferably comprises a Fresnel hologram, which enables
a lens to be encoded and which has the further advantage of allowing an
image to be displayed without a conjugate image (with a Fourier hologram
with binary modulation half the available light goes into this conjugate
image, as described above). Like a Fourier hologram with a Fresnel
hologram the displayed image is still in focus substantially irrespective
of distance from the holographic projector.

[0011]In some preferred embodiments the hologram processor implements an
OSPR--type procedure, as described above. However other procedures may
also be employed for calculating the displayed hologram and embodiments
of the invention are not restricted to any particular hologram
calculation technique.

[0012]In another aspect the invention provides an optical module for a
holographic projection system, the module comprising: an optical input; a
spatial light modulator (SLM) for displaying a hologram, said SLM having
an input optical path from said optical input passing through said SLM to
provide a modulatable optical output; a reflector to one side of SLM such
that said optical path through said SLM passes through said SLM twice,
said optical input to said SLM and said optical output from said SLM
being on the same side of said SLM; and demagnification optics coupled to
said modulatable optical output to enlarge an image generated by a
hologram modulating said SLM.

[0013]In some preferred embodiments of the above aspect and a previously
described aspect of the invention, the optical input comprises an optical
light guide such as a fibre optic. Then the optical path diverges from an
output of the light guide, preferably substantially continuously up to
the SLM.

[0014]The above described aspects of the invention, and features of the
above described aspects may be combined in any permutation.

[0015]The invention further provides a consumer electronic device, in
particular a portable device, including a holographic image projection
system or optical module as described above.

BRIEF DESCRIPTION OF THE DRAWINGS

[0016]These and other aspects of the invention will now be further
described, by way of example only, with reference to the accompanying
figures in which:

[0018]FIG. 2 shows an example of an optical system for the holographic
projection module of FIG. 1;

[0019]FIG. 3 shows a block diagram of an embodiment of a hardware
accelerator for the holographic image display system of FIGS. 1 and 2;

[0020]FIG. 4 shows the operations performed within an embodiment of a
hardware block as shown in FIG. 3;

[0021]FIG. 5 shows the energy spectra of a sample image before and after
multiplication by a random phase matrix.

[0022]FIG. 6 shows an embodiment of a hardware block with parallel
quantisers for the simultaneous generation of two sub-frames from the
real and imaginary components of the complex holographic sub-frame data
respectively.

[0025]FIG. 9 shows an embodiment of hardware which performs a 2-D
transform on incoming phase-modulated image data, Gxy, by means of a
1-D transform block with feedback, to produce holographic data guv;

[0026]FIGS. 10a to 10c show, respectively, a conceptual diagram of an
optical system according to an embodiment of the invention, and first and
second examples of holographic image projection systems according to
embodiments of the invention;

[0027]FIGS. 11a to 11e show, respectively, a Fresnel diffraction geometry
in which a hologram h(x,y) is illuminated by coherent light, and an image
H(u,v) is formed at a distance z by Fresnel (or near-field) diffraction,
a Fourier hologram, a Fresnel hologram, a simulated replay field of a
Fourier hologram, and a simulated replay field of a Fresnel hologram
showing absence of a conjugate image from the diffracted near-field, in
which the hologram pixels are 40 μm square, and the propagation
distance z=200 mm;

[0028]FIG. 12 shows change in replay field size caused by a variable
demagnification assembly of lenses L3 and L4 in which in a
first configuration the demagnification is

D = f 3 f 4 , ##EQU00001##

with a corresponding replay field (RPF) size Rmax in which in a
second configuration the demagnification is

D = f 3 f 4 ##EQU00002##

giving rise to a RPF of size R;

[0029]FIGS. 13a to 13c show experimental results for variable
demagnification as illustrated in FIG. 12 for f3=100 mm, f3=200
mm, and f3=400 mm respectively, in which the change in size of the
replay field is determined by the focal length of lens L3, which is
encoded onto the hologram;

[0030]FIG. 14 shows an optical arrangement according to an embodiment of
the invention for a lens-sharing projector design, utilizing a f=100 mm
lens encoded onto a Fresnel hologram displayed on an SLM, in which
(optional) polarisers have been are omitted for clarity; and

[0031]FIG. 15 shows experimental results from the lens-sharing projector
setup of FIG. 14, in which the demagnification caused by the combination
of L4 and the hologram has caused optical enlargement of the RPF by
a factor of approximately three.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0032]We have previously described, in UK patent application number
0512179.3 filed 15 Jun. 2005, incorporated by reference, a holographic
projection module comprising a substantially monochromatic light source
such as a laser diode; a spatial light modulator (SLM) to (phase)
modulate the light to provide a hologram for generating a displayed
image; and a demagnifying optical system to increase the divergence of
the modulated light to form the displayed image. Absent the demagnifying
optics the size (and distance from the SLM) of a displayed image depends
on the pixel size of the SLM, smaller pixels diffracting the light more
to produce a larger image. Typically an image would need to be viewed at
a distance of several metres or more. The demagnifying optics increase
the diffraction, thus allowing an image of a useful size to be displayed
at a practical distance. Moreover the displayed image is substantially
focus-free: that is the image is substantially in focus over a wide range
or at all distances from the projection module.

[0033]A wide range of different optical arrangements can be used to
achieve this effect but one particularly advantageous combination
comprises first and second lenses with respective first and second focal
lengths, the second focal length being shorter than the first and the
first lens being closer to the spatial light modulator (along the optical
path) than the second lens. Preferably the distance between the lenses is
substantially equal to the sum of their focal distances, in effect
forming a (demagnifying) telescope. In some embodiments two positive
(i.e., converging) simple lenses are employed although in other
embodiments one or more negative or diverging lenses may be employed. A
filter may also be included to filter out unwanted parts of the displayed
image, for example a bright (zero order) undiffracted spot or a repeated
first order image (which may appear as an upside down version of the
displayed image).

[0034]This optical system (and those described later) may be employed with
any type of system or procedure for calculating a hologram to display on
the SLM in order to generate the displayed image. However we have some
particularly preferred procedures in which the displayed image is formed
from a plurality of holographic sub-images which visually combine to give
(to a human observer) the impression of the desired image for display.
Thus, for example, these holographic sub-frames are preferably temporally
displayed in rapid succession so as to be integrated within the human
eye. The data for successive holographic sub-frames may be generated by a
digital signal processor, which may comprise either a general purpose DSP
under software control, for example in association with a program stored
in non-volatile memory, or dedicated hardware, or a combination of the
two such as software with dedicated hardware acceleration. Preferably the
SLM comprises a reflective SLM (for compactness) but in general any type
of pixellated microdisplay which is able to phase modulate light may be
employed, optionally in association with an appropriate driver chip if
needed.

[0035]Referring now to FIG. 1, this shows an example a consumer electronic
device 10 incorporating a hardware projection module 12 to project a
displayed image 14. Displayed image 14 comprises a plurality of
holographically generated sub-images each of the same spatial extent as
displayed image 14, and displayed rapidly in succession so as to give the
appearance of the displayed image. Each holographic sub-frame is
generated along the lines described below. For further details reference
may be made to GB 0329012.9 (ibid).

[0036]FIG. 2 shows an example optical system for the holographic
projection module of FIG. 1. Referring to FIG. 2, a laser diode 20 (for
example, at 532 nm), provides substantially collimated light 22 to a
spatial light modulator 24 such as a pixellated liquid crystal modulator.
The SLM 24 phase modulates light 22 with a hologram and the phase
modulated light is provided a demagnifying optical system 26. In the
illustrated embodiment, optical system 26 comprises a pair of lenses 28,
30 with respective focal lengths f1, f2, f1<f2,
spaced apart at distance f1+f2. Optical system 26 increases the
size of the projected holographic image by diverging the light forming
the displayed image, as shown.

[0037]Still referring to FIG. 2, in more detail lenses L1 and L2
(with focal lengths f1 and f2 respectively) form the
beam-expansion pair. This expands the beam from the light source so that
it covers the whole surface of the modulator.

[0038]Lens pair L3 and L4 (with focal lengths f3 and
f4 respectively) form a demagnification lens pair. This effectively
reduces the pixel size of the modulator, thus increasing the diffraction
angle. As a result, the image size increases. The increase in image size
is equal to the ratio of f3 to f4, which are the focal lengths
of lenses L3 and L4 respectively.

[0039]Continuing to refer to FIG. 2, a digital signal processor 100 has an
input 102 to receive image data from the consumer electronic device
defining the image to be displayed. The DSP 100 implements a procedure
(described below) to generate phase hologram data for a plurality of
holographic sub-frames which is provided from an output 104 of the DSP
100 to the SLM 24, optionally via a driver integrated circuit if needed.
The DSP 100 drives SLM 24 to project a plurality of phase hologram
sub-frames which combine to give the impression of displayed image 14 in
the replay field (RPF).

[0040]The DSP 100 may comprise dedicated hardware and/or Flash or other
read-only memory storing processor control code to implement a hologram
generation procedure, in preferred embodiments in order to generate
sub-frame phase hologram data for output to the SLM 24.

[0041]We now describe a preferred procedure for calculating hologram data
for display on SLM 24. We refer to this procedure, in broad terms, as One
Step Phase Retrieval (OSPR), although strictly speaking in some
implementations it could be considered that more than one step is
employed (as described for example in GB0518912.1 and GB0601481.5,
incorporated by reference, where "noise" in one sub-frame is compensated
in a subsequent sub-frame).

[0042]Thus we have previously described, in UK Patent Application No.
GB0329012.9, filed 15 Dec. 2003, a method of displaying a holographically
generated video image comprising plural video frames, the method
comprising providing for each frame period a respective sequential
plurality of holograms and displaying the holograms of the plural video
frames for viewing the replay field thereof, whereby the noise variance
of each frame is perceived as attenuated by averaging across the
plurality of holograms.

[0043]Broadly speaking in our preferred method the SLM is modulated with
holographic data approximating a hologram of the image to be displayed.
However this holographic data is chosen in a special way, the displayed
image being made up of a plurality of temporal sub-frames, each generated
by modulating the SLM with a respective sub-frame hologram. These
sub-frames are displayed successively and sufficiently fast that in the
eye of a (human) observer the sub-frames (each of which have the spatial
extent of the displayed image) are integrated together to create the
desired image for display.

[0044]Each of the sub-frame holograms may itself be relatively noisy, for
example as a result of quantising the holographic data into two (binary)
or more phases, but temporal averaging amongst the sub-frames reduces the
perceived level of noise. Embodiments of such a system can provide
visually high quality displays even though each sub-frame, were it to be
viewed separately, would appear relatively noisy.

[0045]A scheme such as this has the advantage of reduced computational
requirements compared with schemes which attempt to accurately reproduce
a displayed image using a single hologram, and also facilitate the use of
a relatively inexpensive SLM.

[0046]Here it will be understood that the SLM will, in general, provide
phase rather than amplitude modulation, for example a binary device
providing relative phase shifts of zero and π (+1 and -1 for a
normalised amplitude of unity). In preferred embodiments, however, more
than two phase levels are employed, for example four phase modulation
(zero, π/2, π, 3π/2), since with only binary modulation the
hologram results in a pair of images one spatially inverted in respect to
the other, losing half the available light, whereas with multi-level
phase modulation where the number of phase levels is greater than two
this second image can be removed. Further details can be found in our
earlier application GB0329012.9 (ibid), hereby incorporated by reference
in its entirety.

[0047]Although embodiments of the method are computationally less
intensive than previous holographic display methods it is nonetheless
generally desirable to provide a system with reduced cost and/or power
consumption and/or increased performance. It is particularly desirable to
provide improvements in systems for video use which generally have a
requirement for processing data to display each of a succession of image
frames within a limited frame period.

[0048]We have also described, in GB0511962.3, filed 14 Jun. 2005, a
hardware accelerator for a holographic image display system, the image
display system being configured to generate a displayed image using a
plurality of holographically generated temporal sub-frames, said temporal
sub-frames being displayed sequentially in time such that they are
perceived as a single reduced-noise image, each said sub-frame being
generated holographically by modulation of a spatial light modulator with
holographic data such that replay of a hologram defined by said
holographic data defines a said sub-frame, the hardware accelerator
comprising: an input buffer to store image data defining said displayed
image; an output buffer to store holographic data for a said sub-frame;
at least one hardware data processing module coupled to said input data
buffer and to said output data buffer to process said image data to
generate said holographic data for a said sub-frame; and a controller
coupled to said at least one hardware data processing module to control
said at least one data processing module to provide holographic data for
a plurality of said sub-frames corresponding to image data for a single
said displayed image to said output data buffer.

[0049]In this preferably a plurality of the hardware data processing
modules is included for processing data for a plurality of the sub-frames
in parallel. In preferred embodiments the hardware data processing module
comprises a phase modulator coupled to the input data buffer and having a
phase modulation data input to modulate phases of pixels of the image in
response to an input which preferably comprises at least partially random
phase data. This data may be generated on the fly or provided from a
non-volatile data store. The phase modulator preferably includes at least
one multiplier to multiply pixel data from the input data buffer by input
phase modulation data. In a simple embodiment the multiplier simply
changes a sign of the input data.

[0050]An output of the phase modulator is provided to a space-frequency
transformation module such as a Fourier transform or inverse Fourier
transform module. In the context of the holographic sub-frame generation
procedure described later these two operations are substantially
equivalent, effectively differing only by a scale factor. In other
embodiments other space-frequency transformations may be employed
(generally frequency referring to spatial frequency data derived from
spatial position or pixel image data). In some preferred embodiments the
space-frequency transformation module comprises a one-dimensional Fourier
transformation module with feedback to perform a two-dimensional Fourier
transform of the (spatial distribution of the) phase modulated image data
to output holographic sub-frame data. This simplifies the hardware and
enables processing of, for example, first rows then columns (or vice
versa).

[0051]In preferred embodiments the hardware also includes a quantiser
coupled to the output of the transformation module to quantise the
holographic sub-frame data to provide holographic data for a sub-frame
for the output buffer. The quantiser may quantise into two, four or more
(phase) levels. In preferred embodiments the quantiser is configured to
quantise real and imaginary components of the holographic sub-frame data
to generate a pair of sub-frames for the output buffer. Thus in general
the output of the space-frequency transformation module comprises a
plurality of data points over the complex plane and this may be
thresholded (quantised) at a point on the real axis (say zero) to split
the complex plane into two halves and hence generate a first set of
binary quantised data, and then quantised at a point on the imaginary
axis, say 0j, to divide the complex plane into a further two regions
(complex component greater than 0, complex component less than 0). Since
the greater the number of sub-frames the less the overall noise this
provides further benefits.

[0052]Preferably one or both of the input and output buffers comprise
dual-ported memory. In some particularly preferred embodiments the
holographic image display system comprises a video image display system
and the displayed image comprises a video frame.

[0053]In an embodiment, the various stages of the hardware accelerator
implement a variant of the algorithm given below, as described later. The
algorithm is a method of generating, for each still or video frame
I=Ixy, sets of N binary-phase holograms h.sup.(1) . . . h.sup.(N).
Statistical analysis of the algorithm has shown that such sets of
holograms form replay fields that exhibit mutually independent additive
noise.

[0054]Step 1 forms N targets Gxy.sup.(n) equal to the amplitude of
the supplied intensity target Ixy, but with independent
identically-distributed (i.i.t.), uniformly-random phase. Step 2 computes
the N corresponding full complex Fourier transform holograms
guv.sup.(n). Steps 3 and 4 compute the real part and imaginary part
of the holograms, respectively. Binarisation of each of the real and
imaginary parts of the holograms is then performed in step 5:
thresholding around the median of muv.sup.(n) ensures equal numbers
of -1 and 1 points are present in the holograms, achieving DC balance (by
definition) and also minimal reconstruction error. In an embodiment, the
median value of muv.sup.(n) is assumed to be zero. This assumption
can be shown to be valid and the effects of making this assumption are
minimal with regard to perceived image quality. Further details can be
found in the applicant's earlier application (ibid), to which reference
may be made.

[0055]FIG. 3 shows a block diagram of an embodiment of a hardware
accelerator for the holographic image display system of the module 12 of
FIG. 1. The input to the system is preferably image data from a source
such as a computer, although other sources are equally applicable. The
input data is temporarily stored in one or more input buffer, with
control signals for this process being supplied from one or more
controller units within the system. Each input buffer preferably
comprises dual-port memory such that data is written into the input
buffer and read out from the input buffer simultaneously. The output from
the input buffer shown in FIG. 1 is an image frame, labelled I, and this
becomes the input to the hardware block. The hardware block, which is
described in more detail using FIG. 2, performs a series of operations on
each of the aforementioned image frames, I, and for each one produces one
or more holographic sub-frames, h, which are sent to one or more output
buffer. Each output buffer preferably comprises dual-port memory. Such
sub-frames are outputted from the aforementioned output buffer and
supplied to a display device, such as a SLM, optionally via a driver
chip. The control signals by which this process is controlled are
supplied from one or more controller unit. The control signals preferably
ensure that one or more holographic sub-frames are produced and sent to
the SLM per video frame period. In an embodiment, the control signals
transmitted from the controller to both the input and output buffers are
read/write select signals, whilst the signals between the controller and
the hardware block comprise various timing, initialisation and
flow-control information.

[0056]FIG. 4 shows an embodiment of a hardware block as described in FIG.
3, comprising a set of hardware elements designed to generate one or more
holographic sub-frames for each image frame that is supplied to the
block. In such an embodiment, preferably one image frame, Ixy, is
supplied one or more times per video frame period as an input to the
hardware block. The source of such image frames may be one or more input
buffers as shown in FIG. 3. Each image frame, Ixy, is then used to
produce one or more holographic sub-frames by means of a set of
operations comprising one or more of: a phase modulation stage, a
space-frequency transformation stage and a quantisation stage. In
embodiments, a set of N sub-frames, where N is greater than or equal to
one, is generated per frame period by means of using either one
sequential set of the aforementioned operations, or a several sets of
such operations acting in parallel on different sub-frames, or a mixture
of these two approaches.

[0057]The purpose of the phase-modulation block shown in the embodiment of
FIG. 4 is to redistribute the energy of the input frame in the
spatial-frequency domain, such that improvements in final image quality
are obtained after performing later operations.

[0058]FIG. 5 shows an example of how the energy of a sample image is
distributed before and after a phase-modulation stage in which a random
phase distribution is used. It can be seen that modulating an image by
such a phase distribution has the effect of redistributing the energy
more evenly throughout the spatial-frequency domain.

[0059]The quantisation hardware that is shown in the embodiment of FIG. 4
has the purpose of taking complex hologram data, which is produced as the
output of the preceding space-frequency transform block, and mapping it
to a restricted set of values, which correspond to actual phase
modulation levels that can be achieved on a target SLM. In an embodiment,
the number of quantisation levels is set at two, with an example of such
a scheme being a phase modulator producing phase retardations of 0 or
π at each pixel.

[0060]In other embodiments, the number of quantisation levels,
corresponding to different phase retardations, may be two or greater.
There is no restriction on how the different phase retardations levels
are distributed--either a regular distribution, irregular distribution or
a mixture of the two may be used. In preferred embodiments the quantiser
is configured to quantise real and imaginary components of the
holographic sub-frame data to generate a pair of sub-frames for the
output buffer, each with two phase-retardation levels. It can be shown
that for discretely pixellated fields, the real and imaginary components
of the complex holographic sub-frame data are uncorrelated, which is why
it is valid to treat the real and imaginary components independently and
produce two uncorrelated holographic sub-frames.

[0061]FIG. 6 shows an embodiment of the hardware block described in FIG. 3
in which a pair of quantisation elements are arranged in parallel in the
system so as to generate a pair of holographic sub-frames from the real
and imaginary components of the complex holographic sub-frame data
respectively.

[0062]There are many different ways in which phase-modulation data, as
shown in FIG. 4, may be produced. In an embodiment, pseudo-random
binary-phase modulation data is generated by hardware comprising a shift
register with feedback and an XOR logic gate. FIG. 7 shows such an
embodiment, which also includes hardware to multiply incoming image data
by the binary phase data. This hardware comprises means to produce two
copies of the incoming data, one of which is multiplied by -1, followed
by a multiplexer to select one of the two data copies. The control signal
to the multiplexer in this embodiment is the pseudo-random binary-phase
modulation data that is produced by the shift-register and associated
circuitry, as described previously.

[0063]In another embodiment, pre-calculated phase modulation data is
stored in a look-up table and a sequence of address values for the
look-up table is produced, such that the phase-data read out from the
look-up table is random. In this embodiment, it can be shown that a
sufficient condition to ensure randomness is that the number of entries
in the look-up table, N, is greater than the value, m, by which the
address value increases each time, that m is not an integer factor of N,
and that the address values `wrap around` to the start of their range
when N is exceeded. In a preferred embodiment, N is a power of 2, e.g.
256, such that address wrap around is obtained without any additional
circuitry, and m is an odd number such that it is not a factor of N.

[0064]FIG. 8 shows suitable hardware for such an embodiment, comprising a
three-input adder with feedback, which produces a sequence of address
values for a look-up table containing a set of N data words, each
comprising a real and imaginary component. Input image data, Ixy, is
replicated to form two identical signals, which are multiplied by the
real and imaginary components of the selected value from the look-up
table. This operation thereby produces the real and imaginary components
of the phase-modulated input image data, Gxy, respectively. In an
embodiment, the third input to the adder, denoted n, is a value
representing the current holographic sub-frame. In another embodiment,
the third input, n, is omitted. In a further embodiment, m and N are both
be chosen to be distinct members of the set of prime numbers, which is a
strong condition guaranteeing that the sequence of address values is
truly random.

[0065]FIG. 9 shows an embodiment of hardware which performs a 2-D FFT on
incoming phase-modulated image data, Gxy, as shown in FIG. 4. In
this embodiment, the hardware to perform the 2-D FFT operation comprises
a 1-D FFT block, a memory element for storing intermediate row or column
results, and a feedback path from the output of the memory to one input
of a multiplexer. The other input of this multiplexer is the
phase-modulated input image data, Gxy, and the control signal to the
multiplexer is supplied from a controller block as shown in FIG. 4. Such
an embodiment represents an area-efficient method of performing a 2-D FFT
operation.

[0066]In other implementations the operations illustrated in FIGS. 4
and/or 6 may be implemented partially or wholly in software, for example
on a general purpose digital signal processor.

Lens Encoding

[0067]FIG. 10a shows a conceptual diagram of an embodiment of a
holographic display device using a reflective spatial light modulator,
illustrating sharing of the lenses for the beam expander and
demagnification optics. In particular lenses L2 and L3 of FIG.
2 are shared, implemented as a single, common lens which, in embodiments
is encoded into the hologram displayed on the reflective SLM. Thus one
embodiment of a practical, physical system is shown in FIG. 10b, in which
a polariser is included to suppress interference between light travelling
in different directions, that is into and out of the SLM. In the
arrangement of FIG. 10b the laser diode results in a dark patch in the
centre of the image plane and therefore one alternative is to use the
arrangement of FIG. 10c. In the arrangement of FIG. 10c a polarising beam
splitter is used to direct the output, modulated light at 90 degrees on
the image plane, and also to provide the function of the polariser in
FIG. 10b.

[0068]We now describe encoding lens power into the hologram by means of
Fresnel diffraction.

[0069]We have previously described systems using far-field (or Fraunhofer)
diffraction, in which the replay field Fxy and hologram huv are
related by the Fourier transform:

Fxy=F[huv] (1)

[0070]In the near-field (or Fresnel) propagation regime, RPF and hologram
are related by the Fresnel transform which, using the same notation, can
be written as:

Fxy=FR[huv] (2)

[0071]The discrete Fresnel transform, from which suitable binary-phase
holograms can be generated, is now introduced and briefly discussed.

[0072]The Fresnel transform describes the diffracted near field F(x,y) at
a distance z, which is produced when coherent light of wavelength 2
interferes with an object h(u,v). This relationship, and the coordinate
system, is shown in FIG. 11a. In continuous coordinates, the transform is
defined as:

[0074]In effect the factors F.sup.(1) and F.sup.(2) in equation (5) turn
the Fourier transform in a Fresnel transform of the hologram h. The size
of each hologram pixel is Δx×Δy, and the
total size of the hologram is (in pixels) N×M. In equation (7), z
defines the focal length of the holographic lens. Finally, the sample
spacing in the replay field is:

Δ u = λ z N Δ x
Δ v = λ z N Δ y ( 8 )
##EQU00008##

so that the dimensions of the replay field are

λ z Δ x × λ z Δ y
, ##EQU00009##

consistent with the size of replay field in the Fraunhofer diffraction
regime.

[0075]The OSPR algorithm can be generalised to the case of calculating
Fresnel holograms by replacing the Fourier transform step by the discrete
Fresnel transform of equation 5. Comparison of equations 1 and 5 show
that the near-field propagation regime results in very different replay
field characteristics, resulting in two potentially useful effects. These
are demonstrated in FIGS. 11b-11e, which show Fresnel and Fourier binary
holograms calculated using OSPR, and their respective simulated replay
fields.

[0076]The significant advantage associated with binary Fresnel holograms
is that the diffracted near-field does not contain a conjugate image. In
the Fraunhofer diffraction regime the replay field is the Fourier
transform of the real term huv, giving rise to conjugate symmetry.
In the case of Fresnel diffraction, however, equation 5 shows that the
replay field is the Fourier transform of the complex term
Fuv.sup.(2)huv. The differences in the resultant RPFs are
clearly demonstrated in FIGS. 11d and 11e.

[0077]It is also evident from equation 4 that the diffracted field
resulting from a Fresnel hologram is characterised by a propagation
distance z, so that the replay field is formed in one plane only, as
opposed to everywhere where z is greater than the Goodman distance [F.
Wyrowski and O. Bryngdahl, "Speckle-free reconstruction in digital
holography," J. Opt. Soc. Am. A, vol. 6, 1989] in the case of Fraunhofer
diffraction. This indicates that a Fresnel hologram incorporates lens
power, which is reflected in the circular structure of the Fresnel
hologram shown in FIG. 11c. This is particularly useful effect to exploit
in a holographic projection system, since incorporation of lens power
into the hologram means that system cost, size and weight can be reduced.
Furthermore, the focal plane in which the image is formed can also be
altered simply by recalculating the hologram rather than changing the
entire optical design.

[0078]We describe below designs for holographic projection systems which
exploit these advantageous features of Fresnel holograms. There is an
increase SNR penalty but error diffusion may be employed as a method to
mitigate this.

[0079]We next describe variable demagnification.

[0080]Referring back again to FIG. 2, this shows a simple optical
architecture for a holographic projector. The lens pair L1 and
L2 form a Keplerian telescope or beam expander, which expands the
laser beam to capture the entire hologram surface, so that severe
low-pass filtering of the replay field does not result. The reverse
arrangement is used for the lens pair L3 and L4, effectively
demagnifying the hologram and consequently increasing the diffraction
angle. The resultant increase in the replay field size R is termed the
"demagnification" of the system, and is set by the ratio of focal lengths
f4 to f3.

[0081]We have previously demonstrated the operation of a projection system
using a reconfigurable Fourier hologram as the diffracting element.
However, the preceding discussion indicates that it is possible to remove
the lens L3 from the optical system by employing a Fresnel hologram
which encodes the equivalent lens power. The output image from the
projector would still be in-focus at all distances from the output lens
L4, but due to the characteristics of near-field propagation, is
free from the conjugate image artifact. L3 is the larger of the lens
pair, as it has the longer focal length, and removing it from the optical
path significantly reduces the size and weight of the system.

[0082]The use of a reconfigurable Fresnel hologram forms the basis for a
novel variable demagnification effect. The demagnification D, and hence
the size of the replay field at a particular z, is dependent upon the
ratio of focal lengths of L3 and L4. If a dynamically
addressable SLM device is used to display a Fresnel hologram encoding
L3, it is therefore possible to vary the size of the RPF simply by
altering the lens power of the hologram. If the focal length of the
holographic lens L3 is altered to vary the demagnification, then
either the focal length or the position of L4 should also be changed
as shown in FIG. 12. When the focal points of L3 and L4
coincide in a first configuration, the demagnification is at a maximum
value

D max = f 3 f 4 , ##EQU00010##

thus giving rise to a replay field of size Rmax. In a second
configuration, however, the focal lengths f3 and f4 have
changed to f3 and f4 respectively. Since f3<f3,
the demagnification D is now smaller than Dmax. This is compensated
by an increase in f4 so that the focal points of each lens coincide.

[0083]An experimental verification of the variable demagnification
principle was performed using a 100 mm focal length lens in place of
L4. Three Fresnel holograms were calculated using OSPR with N=24
subframes, each of each were designed to form an image in the planes
z=100 mm, z=200 mm and z=400 mm. A CRL Opto Limited (Forth Dimension
Displays Limited, of Scotland, UK) SXGA SLM device with pixel pitch
Δx=Δy=13.62 μm was used to display the
holograms, and the resulting replay fields--projected onto a nondiffusing
screen--were captured with a digital camera. The results are shown in
FIG. 13, and clearly show the replay field scaling caused by the variable
demagnification introduced by each of the Fresnel holograms.

[0084]Preferably, to avoid having to move the lens L4, a variable
focal-length lens is employed. Two examples of such a lens are
manufactured by Varioptic [M. Meister and R. J. Winfield, "Local
improvement of the signal-to-noise ratio for diffractive optical elements
designed by unidirectional optimization methods," Applied Optics, vol.
41, 2002] and Philips [M. P. Chang and O. K. Ersoy, "Iterative
interlacing error diffusion for synthesis of computer-generated
holograms," Applied Optics, vol. 32, 1993]. Both utilise the
electrowetting phenomenon, in which a water drop is deposited on a metal
substrate covered in a thin insulating layer. A voltage applied to the
substrate modifies the contact angle of the liquid drop, thus changing
the focal length. Other, less suitable, liquid lenses have also been
proposed in which the focal length is controlled by the effect of a lever
assembly on the lens aperture size [R. Eschbach, "Comparison of error
diffusion methods for computer-generated holograms," Applied Optics, vol.
30, 1991]. Solid-state variable focal length lenses, using the
birefringence change of liquid crystal material under an applied electric
field, have also been reported [R. Eschbach and Z. Fan, "Complex-valued
error diffusion for off-axis computer-generated holograms," Applied
Optics, vol. 32, 1993, A. A. Falou, M. Elbouz, and H. Hamam, "Segmented
phase-only filter binarized with a new error diffusion approach," Journal
of Optics A: Pure and Applied Optics, vol. 7, 2005, O. B. Frank
Fetthauer, "On the error diffusion algorithm: object dependence of the
quantization noise," Optics Communications, vol. 120, 1995].

[0085]The focal length of the tunable lens is adjusted in response to
changes in f3. An expression for the demagnification for a system
employing a tunable lens in place of L4 can be obtained by
considering the geometry of FIG. 12, in which the total optical path
length is preserved between the two configurations, so that:

f4+f3=f4+f3 (9)

[0086]Using the definitions of D and Dmax, then equation 9 this can
be rearranged to give

D + 1 D max + 1 = f 4 f 4 ( 10 ) ##EQU00011##

[0087]If the Varioptic AMS-1000 tunable focal length lens (which has a
tuning range of 20-25 diopters) is employed, then for f3=100 mm the
demagnification D is continuously variable from 1.8 to 2.5. Care should
be taken to ensure that lens L4 captures as much of the diffracted
field as possible. From equation 8, the Fresnel field is approximately 4
mm square at z=100 mm, which is larger than the effective aperture of the
Varioptic device. As a result, some low-pass filtering of the replay
field is likely to result if this particular device is employed.

[0088]We now describe lens sharing.

[0089]It was shown above that one half of the demagnification lens pair
could be encoded onto the hologram, thereby reducing the lens count of
the projector design by one. It was especially useful that the encoded
lens was the larger of the pair, thus giving rise to a compact optical
system.

[0090]The same technique can also be applied to the beam-expansion lens
pair L1 and L2, which perform the reverse function to the pair
L and L4. It is therefore possible to share a lens between the
beam-expansion and demagnification assemblies, which can be represented
as lens function encoded onto a Fresnel hologram. This results in a
holographic projector which requires only two small, short focal length
lenses. The remaining lenses are encoded onto a hologram, which is used
in a reflective configuration.

[0091]An experimental projector was constructed to demonstrate the
lens-sharing technique, and the optical configuration is shown in FIG.
14. A fibre-coupled laser was used to illuminate a CRL Opto reflective
SLM, which displayed N=24 sets of Fresnel holograms each with z=100 mm.
Since the light from the fiber end was highly divergent, this removed the
need for lens L1. The output lens L4 had a focal length of f=36
mm, giving a demagnification D of approximately three. Polarisers were
used to remove the large zero order associated with Fresnel diffraction,
but have been omitted from FIG. 14 for clarity. The angle of reflection
was also kept small to avoid defocus aberrations.

[0092]An example image, projected on a screen and captured in low-light
conditions with a digital camera, is shown in FIG. 15. The replay field
has been optically enlarged by factor of approximately three by the
demagnification of the hologram pixels and, as the architecture is
functionally equivalent to the simple holographic projector of FIG. 2,
the image is in focus at all points and without conjugate image.

[0093]We next briefly discuss the SNR (signal-to-noise ratio) of images
formed by Fresnel holograms.

[0094]Fresnel holograms have properties which are particularly
advantageous for the design of a holographic projector. However, there is
an associated cost associated with encoding a lens function onto a
hologram, which manifests itself as a degradation of RPF SNR: Taking the
real (or imaginary) part of a complex Fourier hologram does not introduce
quantisation noise into the replay field--instead, a conjugate image
results. This is not true in the Fresnel regime, however, because the
Fresnel transform is not conjugate symmetric. The effect of taking the
real part of a complex Fresnel hologram is to distribute noise, having
the same energy as the desired signal, over the entire replay field.
However it is possible to improve this by using error diffusion; two
example algorithms for the design of Fresnel holograms using a modified
error diffusion algorithm are presented by Fetthauer [L. Ge, M. Duelli,
and R. W. Cohn, "Improved-fidelity error diffusion through blending with
pseudorandom encoding," J. Opt. Soc. Am. A, vol. 17, 2000] and Slack [F.
Fetthauer, S. Weissbach, and O. Bryngdahl, "Equivalence of error
diffusion and minimal average error algorithms," Optics Communications,
vol. 113, 1995]. This shows that a carefully chosen diffusion kernel can
significantly increase the image SNR, thereby offsetting the degradation
due to the use of a Fresnel hologram.

[0095]The use of near-field holography also results in a zero-order which
is approximately the same size as the hologram itself, spread over the
entire replay field rather than located at zero spatial frequency as for
the Fourier case. However this large zero order can be suppressed either
with a combination of a polariser and analyzer or by processing the
hologram pattern [F. Fetthauer and O. Bryngdahl, "Use of error diffusion
with space-variant optimized weights to obtain high-quality quantized
images and holograms," Optics Letters, vol. 23, 1998].

[0096]We next describe an implementation of a hologram processor, in this
example using a modification of the above described OSPR procedure, to
calculate a Fresnel hologram using equation (5).

[0097]Referring back to steps 1 to 5 of the above described OSPR
procedure, step 2 was previously a two-dimensional inverse Fourier
transform. To implement a Fresnel hologram, also encoding a lens, as
described above an inverse Fresnel transform is employed in place of the
previously described inverse Fourier transform. The inverse Fresnel
transform may take the following form (based upon equation (5) above):

F - 1 [ H xy F xy ( 1 ) ] F uv ( 2 ) ##EQU00012##

[0098]Similarly the transform shown in FIG. 4 is a two-dimensional inverse
Fresnel transform (rather than a two-dimensional FFT) and, likewise the
transform in FIG. 6 is a Fresnel (rather than a Fourier) transform. In
the hardware of FIG. 9 the one-dimensional FFT block is replaced by an
FRT (Fresnel transform) block so that the hardware of FIG. 9 performs a
two-dimensional FRT rather than a two-dimensional FFT. Further because of
the scale factors Fxy and Fuv mentioned above, one scale factor
is preferably incorporated within the loop shown in FIG. 9 and a second
multiplies the result.

[0099]Applications for the above described holographic projection system
and/or optics include, but are not limited to the following: a mobile
phone; PDA; laptop; digital still image and/or video camera; games
console; in-car entertainment eg. cinema; personal navigation system (for
example, in-car or wristwatch GPS); displays for automobiles; watch;
personal media player (e.g. MP3 player, personal video player); dashboard
mounted display; laser light show unit; portable or personal video
player/projector; advertising and signage systems; computer (including
desktop); remote control units. A projection system and/or optics as
described above may also be incorporated into an architectural fixture.
In general embodiments of the above described holographic projection
system and/or optics may be incorporated into any device where it is
desirable to share pictures or for more than one person to view an image
at once.

[0100]No doubt many other effective alternatives will occur to the skilled
person. It will be understood that the invention is not limited to the
described embodiments and encompasses modifications apparent to those
skilled in the art lying within the spirit and scope of the claims
appended hereto.

Patent applications in class For synthetically generating a hologram

Patent applications in all subclasses For synthetically generating a hologram